Many nuclei possess a magnetic moment. Nuclear magnetic resonance (NMR) is a phenomenon exhibited by this select group of atomic nuclei (termed "NMR active" nuclei), and is based upon the interaction of the nucleus with an applied, external magnetic field. The magnetic properties of a nucleus are conveniently discussed in terms of two quantities: the magnetogyric ratio (.gamma.) and the nuclear spin (I). When an NMR active nucleus is placed in a magnetic field, its nuclear magnetic energy levels are split into (2I+1) non degenerate energy levels that are separated from each other by an energy that is directly proportional to the strength of the applied magnetic field. This splitting is called the "Zeeman" splitting and is equal to .gamma.h H.sub.0 /2.pi., where h is Planck's constant and H.sub.0 is the strength of the magnetic field. The frequency corresponding to the energy of the Zeeman splitting (.omega..sub.0 =.gamma.H.sub.0) is called the "Larmor frequency". When a bulk sample containing NMR active nuclei is placed within a magnetic field, the nuclear spins distribute themselves among the nuclear magnetic energy levels in accordance with Boltzmann's statistics. This results in a population imbalance between the energy levels and a net nuclear magnetization. It is this net nuclear magnetization that is studied by NMR. Typical NMR active nuclei include .sup.1 H (protons), .sup.13 C, .sup.19 F, and .sup.31 P For these four nuclei I=1/2, and each nucleus has two nuclear magnetic energy levels.
At equilibrium, the net nuclear magnetization is aligned with the external magnetic field and is time-independent. A second magnetic field perpendicular to the first and rotating at or near the Larmor frequency induces a coherent motion (a "nutation") of the net nuclear magnetization. Since, at conventional field strengths, the Larmor frequency is in the MHz range, this second field is called a "radio frequency field" (RF field). The effect of the RF field is to rotate the spin magnetization about the direction of the applied RF field. By convention, an RF pulse of sufficient length to nutate the nuclear magnetization through an angle of 90.degree., or .pi./2 radians, is called a ".pi./2 pulse".
A .pi./2 pulse applied near resonance will rotate the spin magnetization that was along the external magnetic field direction to a plane perpendicular to the external magnetic field. The component of the net magnetization that is transverse to the external magnetic field precesses about the external magnetic field at the Larmor frequency. This precession can be detected with a resonant coil placed such that the precessing magnetization induces a voltage across the coil. Frequently, the "transmitter coil" employed for nutating the spin magnetization and the "receiver coil" for detecting the magnetization are one and the same.
In addition to precessing at the Larmor frequency, the magnetization also undergoes two relaxation processes: (1) dephasing within the transverse plane ("spin-spin relaxation") with an associated relaxation time, T.sub.2, and (2) a return to the equilibrium population of the nuclear magnetic energy levels ("spin lattice relaxation") with an associated relaxation time, T.sub.1.
The nuclear magnetic moment experiences an external magnetic field that is reduced from the actual field due to a screening from the surrounding electron cloud. This screening results in a slight shift of the Larmor frequency (called the "chemical shift" since the size and symmetry of the shielding is dependent on the chemical composition of the sample). This shift is often of interest because it reveals information about the structure of the sample molecules.
In addition to the applied external magnetic field, the nuclei are also subject to local magnetic fields such as those generated by other nearby nuclear magnetic moments and electron magnetic moments. Interactions between these magnetic moments are called "couplings", and one important example of such couplings is the "dipolar" coupling. In solids, the NMR spectra of spin=1/2 nuclei are often dominated by dipolar couplings, and in particular by dipolar couplings to adjacent protons. When the couplings are between nuclei of like kind, these couplings are called homo nuclear couplings. Generally, the effects of these couplings are undesirable because they obscure more interesting, but weaker, phenomena, such as the chemical shifts mentioned above.
In order to reduce the effect of such couplings, a class of experiments employs multiple pulse coherent averaging to continuously modulate the internal Hamiltonians such that, in an interaction frame, selected Hamiltonians are scaled. A sub class of such experiments is designed to reduce the effects of homo nuclear dipolar couplings by reducing the dipolar Hamiltonian to zero in this interaction frame. The most widely used group of these latter experiments consists of long trains of RF pulses applied in quadrature. Data is sampled between groups of pulses. Since upwards of 2,000 RF pulses are applied for a single acquisition, the RF pulses must be carefully aligned to avoid propagation errors.
Four quadrature channels are typically utilized for applying the RF pulses to a sample. By convention, the main static magnetic field is applied along the Z axis, producing a precession of the nuclear spins about the Z axis. In order to more easily discuss the RF pulses, they are normally referenced to a coordinate frame which rotates. The rotating frame is produced by transforming the stationary laboratory coordinate system to a coordinate system that rotates about the Z axis at the Larmor frequency, so transverse magnetization from a spin that is exactly on resonance will appear static in the rotating frame.
The RF pulses are applied to the sample via a coil that produces an oscillating magnetic field that is oriented transverse to the main magnetic field. In the rotating frame, the RF field can be decomposed into components that rotate with the frame and which rotate counter to the frame rotation. The counter rotating component is generally discarded since it is far removed from resonance. So although a single RF coil is employed, the orientation of the RF field (now a static field in the rotating frame) can be varied by a phase shift.
When the RF energy is applied, the nuclear spins rotate an amount depending on the amplitude and length of the RF pulse. The RF pulse length is typically measured by referring to the angle through which the spins are rotated during the application of the RF energy. This latter angle is commonly referred to as a "tip angle". A typical tip angle or pulse length is .pi./2.
RF pulses are never perfect, but the errors have effects of varying severity. The most serious errors are those which result in tip angle deviations from the four quadrature phases (either a miss-setting of the pulse length or of the RF field amplitude) and transient effects associated with the finite rise and fall times of the pulse.
Tip-angle errors can take two forms: (1) the four quadrature RF pulses are set accurately to the same length, but this length deviates from the ideal length of .pi./2; and (2) the length of one or more of the four quadrature pulses deviates from .pi./2 so that the pulses are not of equal length. The second class of errors is more deleterious to line-narrowing experiments than the first.
Since, as previously mentioned, a large number of RF pulses are used for each acquisition, a normal design criterion for the construction of RF pulse cycles is to arrange them to be somewhat self-compensating for common errors mentioned above. Due to symmetries present in the conventional solid echo pulse pair from which most longer cycles are constructed, known cycles are well compensated for a uniform miss-setting of the RF pulse length (which results in a tip angle of other than .pi./2). Therefore, it is more important to insure that the tip-angles produced by the four quadrature pulses are equal to each other than to insure that the tip-angle produced by each pulse be exactly .pi./2.
Present day NMR spectometers generate the basic RF energy from a direct digital synthesizer (DDS) that allows flexible control of both the phase and frequency of the RF energy. For many experiments, the DDS control of the phases is adequate (for instance, virtually all liquid state experiments use only DDS control). However, for the above mentioned homonuclear dipolar decoupling experiments, the phase accuracy and switching speed of the DDS is generally not adequate, and a second analog phase shifter, or quadrature multiplexer is therefore included in series with the output from the DDS. This quadrature multiplexer can very quickly and reproducibly switch the phase of the RF energy between four predetermined settings, thereby producing the required four quadrature channels from a single DDS setting. Since the gating circuit normally used in the multiplexer generally treats all four quadrature pulses nearly the same, the aforementioned tip-angle errors are generally due to errors in the setting of the RF pulse amplitude and not due to miss setting of the RF pulse length.
Consequently, though the conventional quadrature multiplexer is extremely robust and stable, it must be initially aligned so that the RF phases are in quadrature and so that the four RF amplitudes produce a tip angle of exactly .pi./2. This disclosure discusses a new approach to amplitude alignment.
A prior art technique for amplitude alignment is described by B. C. Gerstein et al. in Transient Techniques in NMR of Solids, Academic Press, Orlando, 1985, pp. 215-220. According to this technique, four .pi./2 X pulses are applied, via a single quadrature channel, on resonance to the nuclei of a sample and the magnetization is observed along the Y axis. The four .pi./2 pulses cause the nuclear spins to be rotated successively to positions 90.degree., 180.degree., 270.degree. and 0.degree. from the original Z-axis, and in the Y, Z plane. Data samples are taken between pulses so that the data sampling is effectively at one half of the Nyquist frequency. This sampling rate produces a well-known pattern if the pulse amplitudes are proper. Consequently, the observed magnetization along the Y axis can be used to adjust the RF pulse amplitudes until the pattern appears.
Although it provides no comparison between the amplitudes in different channels, this prior art technique is generally satisfactory for setting the amplitude in a single channel in situations when the RF field is homogeneous over the volume of the sample. For example, in combined rotation and multiple pulse spectroscopy (CRAMPS) experiments, data is normally taken with small spherical samples which occupy very little of the RF coil volume, thereby increasing the RF homogeneity across the sample. In this situation, satisfactory results are obtained with the above-described technique.
However, the prior art technique suffers from two drawbacks. More particularly, in newer applications of multiple pulse techniques, including two-dimensional heteronuclear work and solid state imaging, conditions dictate that the RF field is less homogeneous over the sample volume than in previous experiments.
When the RF homogeneity over the volume of the sample is relatively poor, and the above-described prior art alignment method is used, the magnetization observed during application of the four pulse sequence rapidly decays to zero. As a result, amplitude alignment is difficult and imprecise because the signal decays so rapidly that it is difficult to observe the pattern which is used to adjust the alignment.
Also, with the prior art, the RF amplitudes of the four quadrature channels are set individually to a nominal value of .pi./2 without any effort to set them equal to one another. When they are accurately set to .pi./2, the residual errors are not very important, but when RF inhomogeneity limits the accuracy of the amplitude setting, the errors are scattered about the .pi./2 value and are not the same from channel to channel.
These problems are particularly apparent in solid state imaging, where the trend is to use larger samples and to use as small an RF coil as possible to preserve the RF field strength and to obtain a higher signal-to-noise ratio. The RF inhomogeneity in such conditions is much worse than would be acceptable for CRAMPS work and the prior art alignment technique is difficult to use. However, if the RF fields in the quadrature pulses can accurately aligned at any point in time, such as the beginning of the experiment, then good results are still obtained.
It is a general object of the present invention to provide improved methods for RF field amplitude alignment in an NMR spectrometer.
It is another object of the present invention to provide a method for RF field amplitude alignment in an NMR spectrometer such that the four quadrature RF channels are accurately set to the same amplitude.
It is yet another object of the present invention to provide methods for RF field amplitude alignment in an NMR spectrometer which are independent of RF field inhomogeneity.
It is a further object of the present invention to provide methods for RF field amplitude alignment in an NMR spectrometer which are highly precise and easy to use.
It is still another object of the present invention to provide methods for RF field amplitude alignment in an NMR spectrometer used for two-dimensional heteronuclear experiments, solid state imaging, and other applications requiring a relatively large sample.